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//! # Rotated grids for CMYK halftone dithering and more.
//!
//! This crate provides the [`GridPositionIterator`] type that creates
//! spaced grid positions along a rotated grid.
//!
//! ## Order of generated coordinates
//!
//! Do note that the generation order of the coordinates depends on the specific grid parameters
//! and may not be in the most efficient layout when used directly, depending on your use case.
//! For image processing you may want to prefer a top-down order, in which case you should collect
//! the coordinates into a vector and sort by `y` coordinate first.
//!
//! ## Example
//!
//! ```
//! use rotated_grid::{Angle, GridPoint, GridPositionIterator};
//!
//! const WIDTH: usize = 16;
//! const HEIGHT: usize = 10;
//!
//! let halftone_grids = [
//! ("Cyan", 15.0),
//! ("Magenta", 75.0),
//! ("Yellow", 0.0),
//! ("Black", 45.0),
//! ];
//!
//! for (name, angle) in halftone_grids {
//! println!("{name} at {angle}°");
//!
//! let grid = GridPositionIterator::new(
//! WIDTH as _,
//! HEIGHT as _,
//! 7.0,
//! 7.0,
//! 0.0,
//! 0.0,
//! Angle::<f64>::from_degrees(angle),
//! );
//!
//! let (_, expected_max) = grid.size_hint();
//! let mut count = 0;
//!
//! for GridPoint { x, y } in grid {
//! println!("{x}, {y}");
//! count += 1;
//! }
//!
//! assert!(count <= expected_max.unwrap())
//! }
//! ```
mod angle;
mod point;
pub use angle::Angle;
pub use point::GridPoint;
/// An iterator for positions on a rotated grid.
pub struct GridPositionIterator {
width: f64,
height: f64,
rotated_width: f64,
rotated_height: f64,
dx: f64,
dy: f64,
x0: f64,
y0: f64,
center_x: f64,
center_y: f64,
start_x: f64,
start_y: f64,
sin_alpha: f64,
cos_alpha: f64,
current_x: f64,
current_y: f64,
#[cfg(debug_assertions)]
hits: u64,
#[cfg(debug_assertions)]
misses: u64,
#[cfg(debug_assertions)]
max_repeats: u64,
}
impl GridPositionIterator {
/// Creates a new iterator.
///
/// ## Arguments
/// * `width` - The width of the grid. Must be positive.
/// * `height` - The height of the grid. Must be positive.
/// * `dx` - The spacing of grid elements along the (rotated) X axis.
/// * `dy` - The spacing of grid elements along the (rotated) Y axis.
/// * `x0` - The X offset of the first grid element.
/// * `x1` - The Y offset of the first grid element.
/// * `alpha` - The orientation of the grid.
pub fn new(
width: f64,
height: f64,
dx: f64,
dy: f64,
x0: f64,
y0: f64,
alpha: Angle<f64>,
) -> Self {
assert!(width > 0.0);
assert!(height > 0.0);
let alpha = Self::normalize_angle(alpha.into_radians());
let (sin_alpha, cos_alpha) = alpha.sin_cos();
// Calculate the dimensions of the rotated grid
let rotated_width = (width.abs() * cos_alpha) + (height.abs() * sin_alpha);
let rotated_height = (width.abs() * sin_alpha) + (height.abs() * cos_alpha);
// Calculate the center of the rotated grid.
let center_x = x0 + (width * 0.5);
let center_y = y0 + (height * 0.5);
// Calculate the starting point of the rotated grid.
let start_x = center_x - (rotated_width * 0.5);
let start_y = center_y - (rotated_height * 0.5);
let iterator = GridPositionIterator {
width,
height,
rotated_width,
rotated_height,
dx,
dy,
x0,
y0,
center_x,
center_y,
start_x,
start_y,
sin_alpha,
cos_alpha,
current_x: 0.0,
current_y: 0.0,
#[cfg(debug_assertions)]
hits: 0,
#[cfg(debug_assertions)]
misses: 0,
#[cfg(debug_assertions)]
max_repeats: 0,
};
iterator
}
/// Provides an estimated upper bound for the number of grid points.
/// This is only correct for unrotated grids; rotated grids produce smaller values.
fn estimate_max_grid_points(&self) -> usize {
let num_points_x = (self.width / self.dx).ceil() as usize;
let num_points_y = (self.height / self.dy).ceil() as usize;
num_points_x * num_points_y
}
/// Normalizes the specified angle such that it falls into range -PI/2..PI/2.
fn normalize_angle(mut alpha: f64) -> f64 {
use std::f64::consts::PI;
const HALF_PI: f64 = PI * 0.5;
while alpha >= PI {
alpha -= PI;
}
while alpha >= HALF_PI {
alpha -= HALF_PI;
}
while alpha <= -PI {
alpha += PI;
}
while alpha <= -HALF_PI {
alpha += HALF_PI;
}
alpha
}
}
impl Iterator for GridPositionIterator {
type Item = GridPoint;
fn next(&mut self) -> Option<Self::Item> {
let (sin, cos) = (self.sin_alpha, self.cos_alpha);
let mut repeats = 0;
loop {
let x = self.start_x + self.current_x;
let y = self.start_y + self.current_y;
// Rotate the grid position back to the unrotated frame.
let inv_sin = -sin;
let inv_cos = cos;
let unrotated_x =
(x - self.center_x) * inv_cos - (y - self.center_y) * inv_sin + self.center_x;
let unrotated_y =
(x - self.center_x) * inv_sin + (y - self.center_y) * inv_cos + self.center_y;
// Update the current position.
self.current_x += self.dx;
if self.current_x > self.rotated_width {
self.current_x = 0.0;
self.current_y += self.dy;
}
// Check if the grid position is within the original rectangle.
if unrotated_x >= self.x0
&& unrotated_x <= self.x0 + self.width
&& unrotated_y >= self.y0
&& unrotated_y <= self.y0 + self.height
{
#[cfg(debug_assertions)]
{
self.hits += 1;
}
return Some(GridPoint::new(unrotated_x, unrotated_y));
}
if x > self.start_x + self.rotated_width || y > self.start_y + self.rotated_height {
#[cfg(debug_assertions)]
{
debug_assert!(self.hits as usize <= self.estimate_max_grid_points());
}
return None;
}
#[cfg(debug_assertions)]
{
self.misses += 1;
repeats += 1;
self.max_repeats = repeats.max(self.max_repeats);
}
}
}
fn size_hint(&self) -> (usize, Option<usize>) {
(0, Some(self.estimate_max_grid_points()))
}
}